Noise Reduction in Small Animal PET Images Using a Variational Non-Convex Functional

Positron emission tomography (PET) imaging is widely used in nuclear medicine. However, data acquired by a PET system are generally contaminated with heavy noise, which often persists after image reconstruction. In this paper, a novel non-convex functional is introduced to suitably attenuate noise in PET images. The proposed functional contains a new regularization term defined as a convex combination of two terms: a robust function for border preserving and the L
²
semi-norm. The combination coefficient depends on the gradient of the noisy image, so that it allows a selective smoothing of image regions according to their local characteristics. The proposed method has been qualitatively and quantitatively tested on both simulated and measured data, demonstrating its better performance against well-established methods for PET denoising.